Transistor r-c filters



March 17,v 1970 1 y DQMLUETRECHT 3,501,709

TRANSISTOR R-c FILTERS Original Filed Dec. 2. 1964 .4 Sheets-Sheet 1 D N u u 0 e' H H P1 rr IH u EH# u H LP )n ro 2 rl) d "L En gli fl) i N L9J fo '-1, N

r 9 n (N d' J A r1 Ff rdv) clfs N INVENTOR DALE M.UETRECHT BY M Cb LL ATTORNEYS March 17, 1970 n. M. UETRECHT 3,501,709

TRANSISTOR R-C FILTERS Original Filed Dec. 2, 1964 .4 Sheets-Sheet 2 PIGA '$16.5

INVENTOR DALE M. UETRECHT ATTORNEYS `Match 17, 1970 o.,M.u E1-REH`T 3,501,709

TRANSISTOR no FILTERS Original Filed Dec. 3, 1964 .4 Sheets-Sheet 5 INVENTOR DALE M. UETRECHT MTW ATTORNEYS March 17, v1970l y D. M. UErRl-:CHT 3,501,709

TRANSISTOR R-,C FILTERS Original Filed Deo. z, 1964 .4 Sheets-Sheet 4 Vee Vee

INVENT OR DALE M.UETRECHT BY M Q* Rm,

ATTORNEYS United States Patent O 3,501,709 TRANSISTOR R-C FILTERS Dale M. Uetrecht, Cincinnati, Ohio, assignor to D. H. llidwin Company, Cincinnati, Ohio, a corporation of o Continuation of application Ser. No. 415,236, Dec. 2, 1964. This application Aug. 14, 1968, Ser. No. 754,107

v Int. Cl. H03f 3/04 U.S. Cl. 330-21 1 Claim ABSTRACT F THE DISCLOSURE This application is a continuation of application Ser. No. 415,236, led Dec. 2, 1964, and now abandoned.

The present invention relates generally to active filter networks and more particularly to transistor filter networks having only capacitive reactances in which the component values are selected to provide steep roll off just beyond the filter band pass.

Filters having steep roll off (at least 6 db per octave) in the vicinity of their cut off frequencies have generally, in the past, required an inductance and capacitance. At audio frequencies, however, the use of inductances is generally to be avoided, for economic and space reasons.

The prior art indicates that -lter characteristics substantially the same as those attained with inductance, capacitance networks can be obtained with resistance capacitance networks connected with active elements, such as tubes or transistors. One of the most significant articles on the subject, written by Sallen and Key, appeared on pages 74-85 in the March 1955 issue of the IRE Transactions on Circuit Theory. This article indicates that attainment of filters with high Q values, a necessity in achieving sharp cut off at frequencies just beyond the filter band pass, requires highly stabilized, complicated active elements, and carefully adjusted passive elements having close tolerances. The same article indicates that if these precautions are not taken Qs of only 2 are realized. Also, the idealized responses calculated by Sallen and Key ignore the effects of finite input and output impedance. In mass production circuits adapted for commercial use, it is not practical to employ complicated negative feedback stabilizing circuits or expensive components having eXtreme tolerances. For economic reasons, transistors, elements having input impedances that cannot be ignored, are preferably employed.

According to the present invention, high Q (at least 5) transistorized filters having no inductances are provided in which the circuit values are selected on a predetermined generalized, mathematical basis. Each filter circuit includes two capacity branches and two resistive `ICC branches so that the transfer function denominators can be represented by the form:

D(S)=d0+d1s+d2s2 (l) where: sis the Laplace operator, and do, d1 and d2 are constants. By letting d1 Hm and wlmi/.

Do) -d [1+di4-()2] wo wo (2) where: d=1/Q, and w0=cut off angular frequency of a low or high pass filter and the center frequency of a bandpass or elimination filter. Normalizing Equation 2, D(s) becomes Dn(s)=1+ds+s2 (3) It can be shown that '1 KlRlCi -l-HRiCz'l-B R201 -lKzRzCz where:

R1=resistance of first resistive branch,

R2=`resistance of second resistive branch,

C1|=capacity of first capacitive branch,

Czzcapacity of second capacitive branch,

K1, K2, H and B are all constants dependent upon the transistor and circuit configuration. Equation 4 can be rewritten as:

Thus, R and C are resistance and capacity values necessary to satisfy the relationships for a fand p. It can be shown that the minimum value of d is given by:

I have found that these mathematical concepts enable transistorized low pass, high pass and band pass active filtershaving minimum d values of 0.2 to be attained with resistors and capacitors having 10% tolerances as well as transistors having common emitter current gains (hfe) greater than 15. In many configurations, only a single common collector transistor having a positive feedback network need be employed. Reduction of dmin is attained by modifying the single transistor circuit so the emitter follower output is replaced with a modified Dar- 3 lington circuit in which positive feedback is attained from a second emitter follower stage cascaded with the first emitter follower.

dmm can also be reduced, according to the present invention, by connecting a common base transistor in the base circuit of a positive voltage feedback circuit. The base of the emitter follower is connected in a positive feedback network to the emitter of the common base transistor. When this configuration is employed as a low pass filter, each of the feedback impedances is a capacitor. Further reduction of dmm in this embodiment is also attained by employing the modied Darlington network.

In the positive feedback embodiments, no stability problems arise because the feedback magnitude cannot exceed unity. Unity gain cannot be exceeded since the output voltage of an emitter follower can never be greater than its base input voltage and the output current of a common base transistor cannot exceed its emitter input current.

The generalized teachings of the present invention can also be extended to transistorized, active bandpass filters employing negative, D.C. stabilizing feedback networks. The negative feedback networks, however, generally require transistors with appreciably larger values of hfe than is required with the positive feedback arrangements.

It is, accordingly, an object of the present invention to provide new and improved active filter networks employing only capacitive reactances.

It is another object of the invention to provide new and improved, transistorized active filters, requiring no inductances and having resistances and capacitances selected in a predetermined manner to provide maximum Q. v

An additional object of the invention is to provide new and improved high Q transistorized active filters requiring no inductances and utilizing components having standard tolerances. p

A further object of the invention is to provided transistorized active filters requiring no inductances or complicated stabilizing networks and having Qs on the order of at least 5.

It is another object of the invention to provide transistorized active filters employing only capactive reactances in which maximum possible values of Q are attained by utilizing predetermined component values.

A further object of the invention is to provide a transistorized active filter requiring no inductances, which filter employs a pair of stabilized positive feedback networks.

Still another object of the invention is to provide an active filter that is inexpensive since it uses a minimum number of conponents and transistors having values of hfe in excess of l5.

The above and still further objects, features and advantages of the present invention will become apparent upon consideration of the following detailed description of one specific embodiment thereof, especially when taken in conjunction with the accompanying drawings, wherein:

FIGURES 1, 2 and 3 are circuit diagrams for the common collector, common emitter and common base circuits, respectively;

FIGURES la, 2a and 3a are the equivalent circuits of FIGURES 1, 2 and 3, respectively;

FIGURES 4-7 are circuit diagrams illustrating different embodiments of low pass filters according to the present invention;

FIGURES 8 and 9 are circuit diagrams for different embodiments of high pass filters according to the present invention;

FIGURES 10 and 11 are circuit diagrams of band elimination networks of the present invention;

FIGURES 12 and 13 are circuit diagrams of positive feedback, low pass filters according to the invention;

FIGURE 13a is a circuit diagram of a simple high pass filter that is optimumly connected with the circuits of 4 FIGURES l2 and 13 to convert them into band pass filters; and

FIGURES 14-18 are circuit diagrams of negative feedback, bandpass filters according to the invention.

Many components in the several figures are provided with reference numeral and subscript notations. The same subscript, e.g. R1, is applied to apparently different components in the different figures. However, the common subscripts are utilized to designate the same elements in Equations 4-6.

In FIGURES 1-3, there are illustrated circuit diagrams for PNP transistors 11-13, respectively connected in the conventional common collector, common emitter and common base configurations. In each figure, the input current and voltage are designated I1 and V1 while the output current and voltage are I2 and V2. In FIGURES 1 and 2, the emitter of transistors 11 and 12 are connected through negative feedback resistances, Re, 14 and 15 to ground. In FIGURE 2, the transistor collector is connected to a negative biasing potential via load resistor, Re, 21 while the collector of transistor 11, FIGURE l, is directly connected to the bias source. In both FIGURES l and 2, an audio signal source, such as derived from an electronic organ, is applied between the base of each transistor and ground.

In the common base configuration, FIGURE 3, the audio signal is applied to the emitter base junction of transistor 13 that is shunted by biasing resistor Re, 16. The transistor collector is powered from a negative D.C. supply through load resistor Re, 17.

Conventional hybrid equivalent circuits, FIGURES 2a and 3a, are employed for the common emitter and common base configurations. In each circuit, a number of approximations is made because audio frequency signals are employed as sources and relatively small output impcdances are fed by the transistors. Thus, effects of reverse voltage ratio can be ignored, and it can be assumed that the transistor output impedance introduces zero phase shift.

The common emitter equivalent circuit, FIGURE 2a, comprises an admittance, B1Ge, 18 connected between input terminal 19 and ground and a current generator hfeIl, 22 shunted by load resistor 21 across output terminal 23 and ground. In the common base equivalent circuit of FIGURE 3a, resistance 24, re, is connected between input terminal 25 and ground while the output circuit between terminal 27 and ground comprises current generator 26, hfbKbIl, shunted by load resistor 17.

The common collector equivalent circuit, FIGURE 1a, is a modified hybrid configuration in which input terminal 28 is connected to ground by the parallel combination of admittance 29, BIGe, and current generator 31, B112, that feeds current into node 28. The output circuit between terminal 32 and ground comprises the series combination of resistor 33, re, and voltage source 34, KcVl, having a polarity such that the voltage at its ungrounded end corresponds with the polarity of the input voltage at terminal 28.

In each of FIGURES 1a, 2a and 3a, as well as in the remainder of the specification, like reference letters denote similar circuit parameters. lIn the grounded base configuration, it has been found that the emitter base resistance, re, can be expressed almost independently of the transistor selected in accordance with:

Re-Ve Asoi-src,

z1b=collectoremitter current gain in the common base circuit,

In certain circuit configurations to be described the subscript 1 for B1 is changed to a 2, i.e. B2, and subscripts are added to re, Kc, etc., such as rel, rez, Kel, Keg. ln these instances, more than one transistor is employe-d in the circuit under consideration, and the several transistors are cascaded. The subscript 1 always has reference to parameters of the transistor directly responsive to the input, the subscript 2 to parameters of the second cascaded transistor, i.e. the one directly responsive to the output of the first transistor. The nomenclature is extended so the parameters of the nth cascaded transistor bear the subscript n.

Reference is now made to the low pass lter of FIG- URE 4 wherein an audio source is connected between input terminal 3S and ground. Terminal 3S is connected via series connected resistors 36 and 37, R1 and R2, to the base of emitter follower or common collector PNP transistor 38. A positive feedback path for the voltage developed across emitter resistor 39, Re, is provided with capacitor 41, C1, connected between the transistor emitter and the junction between resistors 36 and 37. Connected between the transistor base and ground is capacitor 42, C2. While the FIGURE 4 circuit contains a positive feedback loop, no possibility of instability arises since feedback cannot exceed -l-l. ThisV is because the emitter feedback voltage can never exceed the base input voltage and it is true of each positive feedback, emitter follower configuration disclosed.

It can be shown that the transfer function between in- I put and output terminals 35 and 43 of the circuit illustrated in FIGURE 4 is represented by:

h Gn s +ds+$2 (12) where d is defined by Equation 4 and hl. The Values of the K1, K2, B and H constants in Equation 4 for the FIGURE 4 configuration are:

K2=1 B=B1(l+) and The values of re and B1 for transistor 38 are identical with those for the common collector equivalent circuit shown in FIGURE 1a. Of course, R1 and R2 are the values of resistors 36 and 37, respectively, 'while C1 and C2 are the values of capacitors 41 and 42, respectively. The cut off frequency of the filter is given by RC r/RlRzcl 2 To provide maximum circuit Q, the value of dmm is selected in accordance with Equation 6. As a practical matter, for the circuits disclosed by FIGURES 5, 6, 8, 9, 1l and 13, where more than one transistor stage is employed, it has been found that dmin must not always he utilized to attain acceptable Qs, i.e. Qs at least equal to 5. Qs on the order of 5 are derived if transistors having hfe values of at least 15 are utilized. However, for the 6 single transistor embodiments illustrated in FIGURES 4, 7, 10 and 12, strict adherence to Equation 6 is necessary.

The circuit of FIGURE 4 can be modified, as shown in FIGURE 5, to provide lower values of d by replacing the single emitter follower stage 38 with a cascaded pair of emitter follower transistors y44 and 45. To minimize the value of re1/Re1 so the required Q values are attained, resistor 46, yR81, in the emitter circuit of transistor 44 is connected to positive D.C. source Vee at terminal `47. It is seen that the value of re1/Re1 is minimized With this configuration when it is considered from Equation 7 that re is inversely related to Vee. -Positive feedback, essentially as shown in FIGURE 4, is derived across load resistor 48, Rs2, that is connected between the emitter of transistor `45 and ground.

The circuit of FIGURE 5 has virtually the same transfer function as the FIGURE 4 configuration, The only distinctions are in the values of K1, and B which have magnitudes indicated by:

Where: re1 and :'92 are respectively the values of re for transistors 44 and 4S in accordance with Equation 7, and

B1 and B2 are respectively values of the transistor parameters for stages 44 and 45, as indicated by B1 in Equation 8.

Reference is now made to the circuit configuration of FIGURE 6 wherein an audio source is applied from terminal 51 to the emitter of grounded base PNP transistor S2 via resistor, Rg, 53. Bias potential for the emitter of transistor 52 is supplied by the positive DC. voltage at terminal 54 through resistor 55, R61. Collector lbias is provided 'by the negative D C. potential at terminal 56 via load resistor 57, R1. Resistor S7 is connected with the base emitter junction of emitter follower transistor 58 in virtually the same manner as resistor 36 is connected to transistor 38, FIGURE 4. In particular, the emitter voltage of transistor 58, developed across resistor 59, Re2, is coupled back to the ibase input resistor 61, R2, via capacitor 62, C1. Shunt capacitor 63, C2, is returned from the base of transistor 58 to the emitter of transistor 52 to provide a positive feedback path that must have a value less than one since the collector current of a grounded base stage is always less than the emitter current.

The low pass transfer function of FIGURE 6 is of exactly the same form as given in Equation 12. The values of the constants differ widely from the low pass circuits of FIGURE 4 and 5 since: v

Again, suitable Q values are attained if transistors 52 and 58 have values of hfe in excess of 15.

ReZ

The circuit of FIGURE 7 is generally preferred over the one of FIGURE 6 since the response is less sensitive to transistor variations and common base transistor 52, in combination with common emitter transistor `65, provides greater isoiation between the summed feedback and input signals.

Reference is now made to FIGURE 8 of the drawings, where there is illustrated a high pass filter having an output-input transfer function given by:

S News (1s) Audio ysignal at terminal 71 is fed to the base of common collector PNP transistor 72 via series connected capaci tors 73 and 7-4, C1 and C2. Base bias for transistor '72 is established by a voltage divider including resistors 75 and 76,

a and 1 a which divider is connected between the negative DC. potential at bus `84 and ground. It is noted that the parallel equivalent resistance of resistances 75 and 76 equals R2, a quantity appearing in basic design Equations 4-6. Positive feedback less than one for the emitter voltage developed across resistor 77, Re, is provided by resistance 78, R1, to the junction of capacitors 73 and 74.

In FIGURE 8, the values of the circuit parameters to define K1, K2, B and H in Equation 5 are given by:

The constant term in the numerator of Equation 9, h, equals 1 and cut orf frequency, W0, equals 1/RC. Suitable Q values are easily obtained by correct selection of the circuit components in accordance with Equation 5 if transistor 72 has an hfe 0f at least l5.

FIGURE 9 is a modification of FIGURE 8 so that the single emitter follower 72 is replaced with cascaded emitter followers 79 and 80. Emitter resistance 81, Rel, for transistor 79 is returned to the D.C. positive bias potential at terminal 82 While feedback is derived from the emitter of transistor 80 across grounded resistoi 83, R22. In FIGURE 9, al1 parameter values are identical with those in FIGURE 8 except K2, B and H which are:

8 There are provided in FIGURES l0 and 11, band elimination filters having an output-input transfer function given by:

tf and p are given supra.

The circuit of FIGURE 10 comprises grounded collector PNP transistor having its base connected to an audio signal source at terminal 86 via the combination of resistor 87, R2, in parallel with series connected capacitors 88 and 89, C1 and C2. A voltage divider including resistances 91 and 92,

and

connects the transistor emitter to ground. The tap between resistors 91 and 92 is connected to the junction of capacitors 88 and 89 to establish a positive feedback network.

The center frequency of the rejection band is given by W0=1/RC while the slope of the filter skirts is inversely related to b. The center frequency attenuation, G (W0), is determined by the ratio b/ d. Therefore, it is necessary that d be 1iarge enough to obtain the desired b/d.

The values of the constants in the FIGURE 10 circuit required to satisfy Equations 5 and l1 are given by:

As in the other embodiments, dmm in the circuit of FIGURE 10 can be decreased by substituting for the single emitter follower, a pair of cascaded emitter followers 93, 94, as shown in FIGURE 11. The emitter of transistor 93 is connected to the positive voltage at terminal 95 via resistance 96 while feedback is from the top of the voltage divider in the emitter circuit of transistor 94. The values used for determining the circuit constants required in FIGURE 11 are:

Reference is now made to the low pass filters of FIG- URES 12 and 13 having transfer functions in accordance with:

where: f is a constant equal to one and each of the other quantities is defined supra. In FIGURE 12, audio input signal is applied to the base of PNP transistor 97 from terminal 98 via resistance 99, R2. The transistor base circuit is shunted by series capacitors 101 and 102, C1 and C2, the tap between which is connected in a positive feedback loop to the transistor emitter via resistor 103, R1. Output and feedback volt-age at the emitter of transistor 97 is derived across resistor 104, Re.

FIGURE 13 is the cascaded emitter follower modification of FIGURE 12 in which emitter biasing voltage for transistor 105 and base biasing voltage for transistor 106 s derived from the positive D C. voltage at terminal 107 via resistor 107, Rel, and feedback voltage is derived across grounded output resistor 108.

The values of K1, K2, B and H for the circuits of FIGURES 12 and 13 are identical with those in the circuits of FIGURES 8 and 9, respectively. For the circuits of FIGURES 12 and 13,

and the cut-off frequency of the passband for these circuits is given by w =1/RC.

In the circuits of FIGURES 4-13, desired Q values are attained with a minimum number of transistors because `Of the positive feedback networks employed. In general, it can be stated that r11/Re should be as small as possible and hn, as large as possible to obtain suitable Qs. Stability is insured, despite positive feedback, because closed loop gain cannot exceed unity.

The high and low pass filters of FIGURES 4-9, 12 and 13 can be cascaded together to provide band pass filters or band pass filters can be formed =by connecting simple, passive high or low pass RC networks in cascade with the outputs of these active filters. I have found, however, that with the embodiments of FIGURES 12 and 13, a band pass filter having the desired d values can be attained by connecting capacitor 151, C3, of the simple RC filter network shown in FIGURE 13a to the emitter 0f transistor 97 or 106. Shunt resistor 152, R2, of the simple filter is connected from capacitor 151 to ground. By selecting C3: (C14-C2) and R3=R1, the constant f term in the numerator of -Equation 16 is eliminated so the band pass transfer function of is attained. In Equation 17 each of the parameters is defined to conform with those set forth for the embodiments of FIGURES 12 and 13.

In negative feedback bandpass circuits having response transfer functions given by:

MSFT# and@ l-aE a the latter also providing negative feedback stabilizing effects. The emitter and collector of transistor 114 are connected to ground and the negative D.C. bias voltage at terminal 118 by negative feedback resistor 120, R91, and load resistor 121, R2, respectively. High frequency attenuation is attained by shunting the path between the collector of transistor 1114 and ground with capacitor 122.

To attain desired values of d in the circuit of FIGUR-E 10 14 in accordance with Equations 4-6, the K1, K2, B and H parameters are given by:

where, by definition:

BlRl) e1 Re1 To enable a circuit similar to that illustrated in FIG- URE 14 to operate satisfactorily with higher impedance sources and lower output impedances, the modification of FIGURE 15 is provided. In FIGURE l5, the negative feedback network comprising resistors 116 and 117, FIG- URE 14, is replaced with emitter follower stage 123 having resistors 124 and 125,

connecting its emitter to the positive biasing potential at terminal 126. The tap between resistors 124 and 125 is connected to the `base of transistor 114 to form negative feedback stabilizing network. In FIGURE 15, the circuit parameters are given by:

where Another manner for attaining bandpass characteristics indicated by Equation 13 with negative feedback is shown in FIGURE 17. Audio signal at terminal' 131 is fed through low frequency attenuating capacitor 132, C1, to the base of common emitter transistor 133, the emitter of which is connected through resistor 134, Rel, to ground. Collector bias for transistor 133 is supplied from the negative, D.C. voltage on bus 135 through load resistor 136, R2. Base bias is provided with the voltage divider comprising resistor 137, R1', the collector emitter path of grounded base transistor 138, and resistor 139 that is connected between the negative and positive supplies at buses 135 and 141. Transistor 138 serves as a signal responsive variable resistor for stabilizing the operating point of transistor 1313 and is controlled in response to the negative feedback voltage applied through resistor 142, R92, to its emitter by the voltage deriving from the emitter of transistor 143. To provide high frequency attenuation, capacitor 144, C2, connects the collector of transistor 133 to ground.

The component parameters to give the required values of d in the FIGURE 17 circuit are:

and

where RIRZ RelReZ B2H2 1 ReZ I2 of the FIGURE 18 circuit are identical with those of -FIGURE 17 except that each occurrence of R62 in the former is replaced with R63 in the latter and I claim:

1. An active filter for audio signal provided by an audio source, said filter having only capacitive reactances, comprising transistor means having an input circuit responsive to said signal, an output circuit, and a feedback circuit between said input and output circuits, said circuits including rst and second resistive branches having values of R1 and R2, respectively, and first and second capacitive branches having values of C1 and C2, respectively, a source of electrode lbiasing potential, biasing resistance means connecting at least one electrode of said transistor with said biasing source, means interconnecting said branches with said transistor means such as to provide a network having a transfer function with a normalized denominator represented by:

where z K1, K2, H and B are predetermined circuit parameter functions of transistor beta and emitter impedance, the biasing resistance means and internal transistor characteristics, the values of the impedances of said branches, the biasing resistance means and the internal characteristics of said transistor means being arranged such that d equals or is less than 0.2, wherein said transistor means comprises a common collector configuration, said first and second resistive branches being connected between said audio source and the base input of said configuration, said first capacitor branch being connected between the emitter output of said configuration and the junction between said resistive branches, said second capacitor branch shunting said base input, and wherein said transistor means further comprises a grounded base transistor stage connecting said audio source to said base input, the emitter of said grounded base stage being connected to be responsive to said audio source and with one end of the second capacitor branch to form a positive feedback loop having gain less than one.

References Cited UNITED STATES PATENTS 2,760,007 8/1956 Lozier 330-28 X 3,124,759 3/1964 Dahlberg 330--25 X 3,331,029 7/ 1967 Banasiewicz et al S30- 25 OTHER REFERENCES Peter G. Sulzer, Junction Transistor, August 1953, Electronics, Figure 3.

ROY LAKE, Primary Examiner S. H. GRIMM, Assistant Examiner U.S. Cl. X.R 

